1. Technical field
The present invention relates a method and device for measuring the relative proportions of plutonium and uranium in a body.
It applies notably to the differentiation of plutonium and uranium contained in large packages of radioactive waste. Large package means concreted waste barrels with a diameter of around one meter or more, or metallic containers whose volumes can be as much as several cubic meters.
It is in fact important, during the storage of radioactive waste, to know the nature and activity of the radioemitters and in particular of the actinides, that is to say essentially uranium and plutonium.
2. Prior Art
The known methods of determining the actinide content of a body can be classified into two categories. In fact the so-called xe2x80x9cdestructivexe2x80x9d methods are distinguished from the so-called xe2x80x9cnon-destructivexe2x80x9d methods.
When destructive methods are used, samples are taken by cutting the package of radioactive material. The samples taken are then analysed using different analysis techniques, amongst which chemical analysis, X-ray fluorescence, gamma spectrometry or neutron activation can be mentioned, for example.
The methods mentioned above are applicable only to samples with a small volume, from a few cubic centimeters to a few liters. They are therefore ineffective for non-destructive measurements of radioactive waste packages of large size.
Amongst the methods of determining the actinide content known as non-destructive, there are also two sub-categories comprising respectively the active non-destructive methods and the passive non-destructive methods.
The passive non-destructive methods are essentially methods of spectrometry of the gamma radiation emitted by the body, counting the neutrons emitted during the spontaneous fission of the actinides contained in the body, or calorimetry.
The method of gamma spectrometry of the radiation emitted is also applicable only to homogeneous samples of small size. This is because counting the neutrons emitted during the spontaneous fission of the actinides in larger samples requires sophisticated equipment, notably for being free of the influence of neutrons coming from sources other than the spontaneous fission of the body to be measured.
The calorimetry method makes it possible to evaluate the total quantity of heat released in a radioactive body, such as a package of waste. It does not however make it possible to determine the type of disintegration which gives rise to the heat.
Finally, active non-destructive methods are known for determining the actinide content of a body. These methods are said to be active because they use a radiation source known as interrogating radiation, external to the radioactive body.
Amongst these active non-destructive methods, there are the measurements of attenuation and the measurements of emitted radiation.
Measurements of attenuation, such as gamma measurement or tomography, measure the attenuation of an external radiation passing through the radio package to be examined. The measurements of emitted radiation, on the other hand, measure a radiation coming from the package itself and caused by an external interrogation radiation. The latter measurements are well adapted to an examination of packages of radioactive waste of large size such as concrete containers. However, the active non-destructive methods known at the present time make it possible only to determine the total quantity of actinides present in a package, without any distinction with regard to their nature or composition. In particular, they do not make it possible to differentiate the uranium from the plutonium contained in the body or radioactive package examined.
The aim of the present invention is an analysis method and device which does not have the limitations mentioned above.
Another obvious aim is to propose a non-destructive measuring method and device which make it possible to differentiate uranium and plutonium in radioactive waste packages.
In order to achieve these aims, the object of the invention is more precisely a method of measuring relative proportions of uranium and plutonium in a body, including the following steps:
a) irradiating the body with photons whose energy is sufficient to cause photofission of actinide elements,
b) counting the number of delayed neutrons emitted per unit time by fission products induced in the said body in response to the irradiation,
c) establishing a time decay function of the number of neutrons ne(t) emitted, characteristic of the actinide composition of the said body,
d) comparing the time decay ne(t) characteristic of the actinide composition of the said body, with time decays of emission of delayed neutrons nu(t), np(t) characteristic respectively of uranium and plutonium, in order to establish the relative proportions of these elements in the body.
Thus the invention is essentially based on the photon activation of the actinides and on the measurement of decrease over time in the number of delayed neutrons.
Unlike neutron activation, which suffers from the short travel of the neutrons in materials containing hydrogen, such as concrete or bitumen, photon activation, used in the method of the invention, proves particularly adapted to waste packages of large size. The attenuation of the photons, notably of the photons with an energy greater than 10 MeV, is in fact low.
Moreover, the detection and counting of delayed fission neutrons has, compared with the counting of prompt neutrons, the advantage of freeing the measurement from the reactions on the nuclei of the matrix containing the radioactive waste. These reactions are in fact added to the phenomenon of photofission of the actinide nuclei during the photon activation.
The prompt neutrons are emitted during fission, and therefore during the gamma irradiation pulse period. The gamma photons also give rise to neutrons, through the neutron-gamma (n, xcex3) reaction induced in the different elements. It is not possible to make a distinction between the prompt fission neutrons and the neutrons originating from the neutron-gamma (n, xcex3) reactions.
The photonuclear reaction of the photons on the actinide nuclei takes place in two steps contained within an interval of time of around one picosecond. A photon is first of all absorbed by the nucleus. The absorbed energy then causes the emission of a photon or one or more particles. When the absorbed energy is greater than the fission threshold of the nucleus it causes on the other hand the fission of the latter.
The effective cross section of absorption of a photon by the atomic nucleus varies with the energy of the photon. For a photon whose energy is less than approximately 6 MeV, very narrow absorption resonances are observed, with a width of approximately 1 eV. On the other hand, for photons with energies greater than 10 MeV, a very broad absorption resonance of several MeV is observed. The absorption resonance energy for photons is respectively 12.26 MeV and 12.24 MeV for uranium 238 and plutonium 239.
The energy of the photons used for irradiating the radioactive body is chosen so as to be sufficient to cause photofission of the actinide elements. In particular, it is chosen so as to be greater than the is photofission threshold, which is situated at approximately 6 MeV. It is preferably chosen so as to be greater than 10 MeV and close to the absorption resonance energy.
The radioactive body is preferably irradiated for a sufficiently long irradiation time to accumulate a sufficient number of fission products and consequently to obtain a significant emission of delayed neutrons. However, it is not necessary to prolong the irradiation unnecessarily. Thus the irradiation time is preferably chosen so as to be around the mean period of the delayed neutrons, that is to say around 10 to 20 seconds, for example.
After the irradiation of the radioactive body to be examined, a counting of the neutrons is effected, preferably in a multiscale mode. The multiscale mode consists of counting the number of neutrons detected in successive intervals of time with a unit width dt. The number of neutrons counted in each interval of time is recorded. The total measuring time xcex94Tm is such that xcex94Tm=Ndt where N is the number of time intervals.
The irradiation and counting steps can if necessary be repeated several times.
A following step of the method consists of establishing, according to the counting, a time decay in the neutrons emitted, characteristic of the fissile material. The time decay can be represented in the form of a curve.
This step can include calculations for correction of the relative abundance of the groups of delayed neutrons according to the experimental conditions and notably the irradiation conditions. The corrections are described below briefly.
It should be stated that, for all the fissile elements, the delayed neutrons are classified into six groups according to their decay periods. The values of these six periods are practically constant for all the fissile elements. On the other hand, the relative abundance of each group varies from one isotope to another. Table 1 gives the relative abundances and periods for uranium 238 and plutonium 239.
The change over time in the number of delayed neutrons emitted by (pure) uranium 238 and (pure) plutonium 239 can be calculated easily, from the data in table 1.
This number is calculated in accordance with the formula:       n    ⁢          (      t      )        =            ∑              k        =        1            6        ⁢                  β        k            ⁢              ⅇ                  -                      λ                          k              t                                          
where xcex2k is the relative abundance of the group k of neutrons and xcexk is the decay constant for the group k.
The relative abundances of the different groups of delayed neutrons correspond to the values at radioactive equilibrium, that is to say quantities accumulated after a very long irradiation, of a duration at least equal to several times the longest period of the group, that is to say at least 5 to 10 minutes.
However, according to a particular aspect of the invention, it is possible to irradiate the radioactive body either continuously or by means of a train of photon pulses.
By way of example, the photons can be delivered in the form of a train of macropulses of duration dt, with a frequency of repetition fr. After a number N of pulses, the radiation is stopped, and the delayed neutrons are counted. If the duration of irradiation is short, radioactive equilibrium is not achieved and the relative abundances are different from those of equilibrium. Hereinafter, an example of calculation of corrections is set out by way of example.
The total number of fissions nf induced in the irradiated sample, by a macropulse, is equal to:
nf="PHgr"xcexa3fdtxe2x80x83xe2x80x83(1)
where "PHgr" is the photon flow, xcexa3f is the effective cross section of photofission, and dt the macropulse duration.
On this number, a fraction xcexdd of delayed neutrons is emitted. The number nk,o of delayed neutrons in the group k (k=1 . . . 6) is equal to:
nk,o=nfxcexddxcex2kxe2x80x83xe2x80x83(2),
where xcex2k is the relative abundance of the group k.
The number of precursors (parent radioactive elements of the delayed neutron emitter), created during a macropulse i, which remain at the end of a sequence of N pulses, is:
nk,i=nk,oexe2x88x92xcexk(Ni)trxe2x80x83xe2x80x83(3)
xcexk being the radioactive constant of the group k, and tr being the repetition period of the macropulses.
The total number of precursors in the group k, at the end of irradiation, is:                               n          k                =                                            ∑                              i                =                1                            N                        ⁢                          n                              k                ,                i                                              =                                    n                              k                ,                0                                      ⁢                                          ∑                                  i                  =                  1                                N                            ⁢                              ⅇ                                                      -                                                                  λ                        k                                            ⁡                                              (                                                  N                          -                          i                                                )                                                                              ⁢                                      t                    r                                                                                                          (        4        )            
Expression (2) standardised to 1 delayed neutron (nfvd=1) gives:
nk,o=xcex2kxe2x80x83xe2x80x83(5)
The sum in expression (4) is reduced as follows:                               S          k                =                                            ∑              i                        ⁢                          exp              ⁡                              [                                                      -                                                                  λ                        k                                            ⁡                                              (                                                  N                          -                          i                                                )                                                                              ⁢                                      t                    r                                                  ]                                              =                                    ⅇ                              N                ⁢                                  xe2x80x83                                ⁢                                  α                  k                                                      ⁢                          ⅇ                              α                k                                      ⁢                                          ∑                i                            ⁢                              exp                ⁡                                  [                                                            α                      k                                        ⁡                                          (                                              i                        -                        1                                            )                                                        ]                                                                                        (        6        )            
xcex1k=xcexktr, where Sk is the correction factor of the number of neutrons in the group k.
The sum in expression (6) is the sum of a geometric series. Calculation gives:                               S          k                =                                            ⅇ                              α                k                                      -                          ⅇ                                                -                                      (                                          N                      -                      1                                        )                                                  ⁢                                  α                  k                                                                                        ⅇ                              α                k                                      -            1                                              (        7        )            
Introducing (5) and (7) into (6) gives:
xcex2k,o=nk=xcex2kskxe2x80x83xe2x80x83(8)
The values of xcex2k,o must be standardised, so that their sum is equal to 1:                                           ∑                          k              =              1                        6                    ⁢                      β                          k              ,              0                                      =        1                            (        9        )            
For calculating the decay of the delayed neutrons, taking account of the irradiation conditions, it is necessary to replace the value xcex2k, in the formula             n      ⁢              (        t        )              =                  ∑                  k          =          1                6            ⁢                        β                      k            ,                          ⁢                  ⅇ                      -                          λ                              k                t                                                          ,
indicated previously, by the value xcex2kSk.
An example of the corrected values for uranium 238 is given in Table 2. The experimental conditions used in the calculation of the corrections are as follows:
duration of a macropulse dt=2.5 xcexcs,
frequency of repetition fr=100 Hz,
irradiation by a series of N=1500 macropulses (irradiation time 15 sec).
When the time decay of the delayed fission neutrons from the fissile material is established, it is compared with the characteristic decay of the neutrons nu(t) and np(t) of pure uranium and plutonium. The characteristic decay of the neutrons of pure uranium and plutonium can be determined experimentally, or calculated directly, for example with the data in Table 1.
According to a particular aspect of the invention, it is possible to determine coefficients a and b such that: ne(t)=anu(t)+bnp(t), the coefficients a and b indicating the relative proportions of uranium and plutonium in the radioactive body.
The coefficients a and b can be determined, for example, by a so-called least squares method set out briefly below.
The decrease in the number of delayed neutrons emitted by the uranium, corrected according to the experimental conditions, is given by the following formula, already explained:                                           n            u                    ⁡                      (            t            )                          =                              ∑            k                    ⁢                                    β              u                        ⁢                          S                              u                ,                k                                      ⁢                          ⅇ                              -                                  λ                                      k                    t                                                                                                          (        1        )            
The number of neutrons emitted by the plutonium is given by the similar formula:             n      p        ⁢          (      t      )        =            ∑      k        ⁢                  β        p            ⁢              S                  p          ,          k                    ⁢              ⅇ                  -                      λ                          k              t                                          
In these formulae the indices u and p of the parameters refer respectively to uranium and plutonium
The total number of neutrons emitted by the mixture is given by the formula:
n(t)=anu+bnpxe2x80x83xe2x80x83(2)
During measurement, the width of the counting interval is xcex94t and the number of intervals is equal to m. The total counting time is therefore equal to:
tm=mxcex94txe2x80x83xe2x80x83(3)
The number of pulses accumulated in an interval i is:                     ci        =                              ∑            1                    ⁢                                    a              1                        ⁢                                          ∑                                  k                  =                  1                                6                            ⁢                                                β                                      1                    ,                    k                                                  ⁢                                  S                                      1                    ,                    k                                                  ⁢                                                      exp                    ⁡                                          (                                                                        -                                                      λ                            k                                                                          ⁢                                                  t                          i                                                                    )                                                        ⁡                                      [                                          1                      -                                              exp                        ⁡                                                  (                                                                                    -                                                              λ                                k                                                                                      ⁢                            Δ                            ⁢                                                          xe2x80x83                                                        ⁢                            t                                                    )                                                                                      ]                                                                                                          (        4        )            
The number of neutrons counted in an interval of time i, during the multiscale counting, is designated by Cei.
The values of a and b are sought, which fulfil the condition:
Cei=cixe2x80x83xe2x80x83(5a),
where ci is defined by formula (4).
This equation, in matrix form, is written generally in the form:
MX=Yxe2x80x83xe2x80x83(5b)
where M, X and Y are the matrices defined as followed:                                           M                          i              ,              1                                =                                    ∑                              k                =                1                            6                        ⁢                          β              ⁢                              xe2x80x83                            ⁢              u                                      ,                            (6a)                                                      M                          i              ,              2                                =                                    ∑                              k                =                1                            6                        ⁢                          β              ⁢                              xe2x80x83                            ⁢              p                                      ,                            (6b)                                          X          =                      (                                                            a                                                                              b                                                      )                          ,                            (6c)                                                      Y            i                    =                      Ce            i                          ,                            (6d)            
The values of Mi,1, Mi,2 and Yi are standardised as follows:                                                         ∑                              i                =                1                            m                        ⁢                          M                              i                ,                1                                              =          1                ,                            (7a)                                                                    ∑                              i                =                1                            m                        ⁢                          M                              i                ,                2                                              =          1                ,                            (7b)                                                                    ∑                              i                =                1                            m                        ⁢                          Y              i                                =          1                ,                            (7c)            
The solution of equation (5b) is:
X=(MTM)xe2x88x921(MTY)xe2x80x83xe2x80x83(8),
From the parameters a and b determined by formula (8), the uranium content xcfx84u is calculated:                                           τ            u                    =                      a                          a              +              b                                      ,                            (9a)            
and that of plutonium xcfx84p:                                           τ            p                    =                      b                          a              +              b                                      ,                            (9b)            
The invention also relates a device for measuring relative proportions of uranium and plutonium in a radioactive package.
The device has:
a source of activation photons for irradiating a radioactive package,
at least one neutron detector, placed in the vicinity of an area for receiving the package, able to deliver counting signals for neutrons emitted by the package,
means of acquiring the counting signals, able to establish a decrease over time in the number of neutrons emitted, characteristic of the radioactive package,
calculation means for comparing the characteristic decay of the radioactive package with the respective characteristic decays of pure uranium and plutonium and in order to establish relative proportions of uranium and plutonium in the package.
The acquisition means and the calculation means can be produced for example in the form of an electronic acquisition card, connected to a microcomputer, with an appropriate calculation program.
According to a particular embodiment of the device, the photon source can include an electron accelerator provided with a Bremsstrahlung target.
According to a preferred implementation, the device can have from 4 to 7 neutron detectors disposed around the area for receiving the radioactive waste package.
The arrangement of the detectors and other characteristics and advantages of the invention will emerge more clearly from the description which follows, with reference to the figures of the accompanying drawings. This description is given by way of purely illustrative and non-limitative example.